I highly recommend all of these games. But, in order of importance, I would say:
1. TrainyardExtremely addictive puzzle game. the difficulty raises from very easy to absurdly difficult at the later stages, and there's unlimited replayability because the online database has millions of user-made maps.
http://www.youtube.com/watch?v=xWtIb7NEYgM2. BattleheartWorth at least one play through; Several more if you love gearing up and levelling up different parties.
3. Where's my Water?Very fun and addictive. It can be challenging at times, especially the achievements, but overall not too hard. They're always adding new levels too.
4. GeodefenseThis tower defense game rocks, as does its sequel GD: Swarm. Unfortunately there's some
Openfeint crap that the game nags you about trying to sign you up for. Just make sure you turn off hardcore mode on your first play through.
5. Cut the RopeThis one's almost exactly like where's my water in terms of layout. Very quick and significantly easier than the above puzzle games.
6. Phoenix Wright: Ace AttorneyThis is a port of the nintendo game. The characters are great and the crime solving puzzles are pretty challenging. However, the dialogue takes a significant amount of time (as it probably should because you have to remember what people say), the game is quite long, and occasionally you will get stuck if you miss something important. It's absolutely worth it if you have the time, and a trilogy package of this game and the next 2 sequels is supposed to be coming out in a few months.